A helicopter includes a plurality of rotor blades that are coupled to, rotate with, and transfer loads to, a hub. Each rotor blade rotates with a constant angular rate Ω, with the root of the blade attached to the hub. With reference to FIG. 1, there is shown a simplified diagram of a helicopter blade rotating around an axis, r. With the blade position for the kth blade regarded as Ψk, the motion of the kth blade includes a flapping angle βk, a lead-lag angle ζk, and a pitch angle θk. If elastic deformations are small, then Bk generally determines the blade tip path.
Loads from the blades are transferred to the hub of the helicopter. If the blades are articulated, then moments acting on the hub are theoretically negligible. The force on the hub of the kth blade can be determined using Equation 1, below:FkH=Xα sin(ψk)+Xαcos(ψk)  Equation 1
Where Xα are the loads along the aircraft's x, y, and z axis and the force due to blade k on the hub is FkH. In the case of identical blades, the sum of all forces on the hub is determined using Equation 2, below:FH=Σk=0B-1FkH=0  Equation 2
Of course, identical blades are theoretical, and deviations from a nominal blade will result in a non-zero force, which is measured as vibration (measured, periodic accelerations) in the helicopter and different blade track height (variations in relative blade height).
The relationship between perturbations between blades and the resulting track deviation and vibration is complex. For example, in a simplified hypothetical, where the mass balance of all blades is identical but the flapping angle, βk, is different, by adjusting pitch of the kth blade an identical track/flapping angle could be reached for a given helicopter airspeed. However, a change in pitch of that blade would set-off a series of consequences such as, affecting the adjusted blade's lift and drag, which would change the blade's lead/lag, that would in turn change the mass balance of the hub, and ultimately result in accelerations that would increase vibration.
The non-uniformity of the blades results in aerodynamic imbalance, mass imbalance, and track errors. Prior art efforts to decrease the non-uniformity of the blades began as efforts to reduce track split, i.e., the maximum difference in blade track height, errors—resulting in “flat track” (in other words, obtaining a minimum difference in blade track height). While a flat track does not always result in a low vibration helicopter, after a blade change or blade balancing, it is essential that the blade track split be within the manufacture's specifications.
To correct for blade non-uniformities, rotor blades are generally manufactured with devices to purposely induce non-uniformities that produce conditions that can be accounted for and that cancel the effect of the naturally occurring blade errors. These devices can include:                1. Weights (WTS), which are attached at specific locations (e.g., hub and rotor tip) to change the blade moment. Weights do not affect blade track height;        2. Pitch control rod (PCR) setting, which by changing length of the pitch rod, changes the angle of attack of that blade relative to the other blades; and/or        3. Trailing edge tabs (TAB), which effectively change the blade's camber when bent. This in turn affects the aerodynamic loads/moments on the blade.        
The acceleration due to blade induced vibration is measured for specific points in the aircraft, such as the Pilot/Copilot vertical acceleration, which can be combined vectorially to derive cockpit vertical (A+B) or cockpit roll (A−B); Cabin Vertical; Cabin Lateral; or other locations where vibration deleteriously effects equipment or passengers.
The magnitude of vibration will also be affected by the regime (airspeed) of the helicopter. For example, there is no flapping motion (βk) when the helicopter is on the ground or hovering, thus removing a component of potential vibration. Thus, typical regimes for helicopter might be: Ground, Hover, 90, 120 and 150 knots.
The maintenance procedure to reduce maximum difference in blade track height (track split) and vibration is called Rotor Track and Balance (RTB). Further information regarding RTB is described in the following publications and patents: Bechhoefer, E., Fang, A., “Rotor Track and Balance Improvements”, Conference of the Prognostics and Health Management Society, 2013; Bechhoefer, E., Fang, A., Van Ness, D., “Improved Rotor Track and Balance Performance Using an Expert System”, IEEE Prognostics Health Management Conference, 2011; Revor, M., Bechhoefer, E., “Rotor Track and Balance Cost Benefit Analysis and Impact on Operational Availability”, American Helicopter Society #60, Baltimore, USA, 2004; Bechhoefer, E., Power, D., “HUMS Rotor Track and Balance Techniques”, IEEE Aerospace Conference, Big Sky, 2003; Bechhoefer, Eric Robert (New Haven, Vt.); “Reducing vibration using QR decomposition and constrained optimization”, Jun. 3, 2003 U.S. Pat. No. 6,574,572; Bechhoefer, Eric Robert (New Haven, Vt.), Ventres, Charles Samuel (Winchester, Mass.), “Reducing vibration using QR decomposition and unconstrained optimization” May 20, 2003, U.S. Pat. No. 6,567,757, each of which is incorporated by reference for its discussion of the same.
Various methodologies have been developed to measure blade track height in an automated fashion. For example, optical tracker systems have been developed for determining the position of a rotating body, with an optical sensor system determining both track height and phase information. These systems are relatively large, heavy, and can, under certain flight conditions, e.g., direct sun light or low contrast conditions, produce significant errors. Alternative designs have included microwave sensing systems where the change in antenna impedance is used to calculate blade track weight and phase information. While solving the low contrast situation found with optical tracking systems, these systems produce large track height errors that limit their usefulness.